We reveal one relationship between each degree algebraic function and its tangent line, via its derivative. In particular, it is easy to see and well known that asymmetry (resp. symmetry) of tangent lines of a quadratic (resp. cubic) function at its minimum and maximum zero points, but it is not easy to investigate symmetry and asymmetry of them of nth-degree functions if n is 4 or more. We thus investigate the relationship between the slopes of the tangent lines at minimum and maximum zero points of the nth-degree function. We will in this note be able to know some sufficient conditions for the ratio of their slopes to be 1 or -1. By these, we can understand that tangent lines at minimum and maximum zero points have a symmetrical (resp. asymmetrical) relationship if the ratio of their slopes is -1 (resp. 1). In other words, these properties give us symmetry and asymmetry of the functions. Furthermore, we also mention the property of the discriminant of a quadratic function.
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